As Bernie Sanders launched a campaign blitz in California on Monday ahead of the state's June 7 primary, his presidential rival Hillary Clinton found herself cancelling appearancesin New Jersey to catch up with him.

Clinton skipped out on plans to campaign in the Garden State on Wednesday and Thursday in favor of a five-day tour through California, where some recent polls have seen her lead on Sanders shrink to a dead heat—though others have put her a few points ahead.

California will be the nation's biggest primary, where 475 delegates are at stake.

Sanders on Monday held a 20,000-person rally in Oakland—which was briefly disrupted by animal rights activists—where he touched on his central campaign platforms, including universal healthcare and free college tuition, and told the crowd, "If we can win here in California, our largest state, one of our most progressive states, we will go into the Democratic Convention with a great deal of momentum and we will come out with the nomination."

"In virtually every state and national poll, we do much better against Trump than does Secretary Clinton," he added.

In fact, Trump and Clinton ranked nearly even in a new national poll released Tuesday, with Clinton's lead in the hypothetical general matchup dwindling over the past week, while Sanders has maintained a 12-point lead over the presumptive Republican nominee.

Sanders' appearance in Oakland comes on the heels of a series of massive rallies across Southern California, including in Santa Barbara, Santa Maria, and Bakersfield. One supporter told the Los Angeles Times, "Bernie just says what relates to us. He doesn't try to relate to us, he gets us."

No matter what happens in California, where Clinton also secured Governor Jerry Brown's endorsement this week, Sanders reiterated that he would stay in the race until the nominating convention in Philadelphia in July.

Clinton "has received obviously a whole lot of superdelegate support, no question about that," Sanders said. "A lot more than I have. But superdelegates don't vote until they’re on the floor of the Democratic convention. That's when they vote." He said he would focus on reminding superdelegates that he is the most formidable candidate against Trump.

"We're going to go in with momentum and we're going to come out with the Democratic nomination," he said.